They are used like you would draw reigns although they attach to the girth straps so more like side reigns. Usually you would have a traditional reign on the gag ring and the other set of traditional reigns on the snaffle. The running reigns take the place of the snaffle reigns. We use these on horses that have a tendancy to leap when checked.
In Argentina we used them on the more spirited horses, which usually meant the ones playing medium/high goal. When I asked I got the simple of 'to stop'!